Title:On the relaxation rate of short chains of rotors interacting with Langevin thermostats

Abstract: In this short note, we consider a system of two rotors, one of which
interacts with a Langevin heat bath. We show that the system relaxes to its
invariant measure (steady state) no faster than a stretched exponential
$\exp(-c t^{1/2})$. This indicates that the exponent $1/2$ obtained earlier by
the present authors and J.-P. Eckmann for short chains of rotors is optimal.